Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-05T05:45:05.582Z Has data issue: true hasContentIssue false

EFFICIENCY IN ESTIMATION UNDER MONOTONIC ATTRITION

Published online by Cambridge University Press:  16 September 2024

Jean-Louis Barnwell
Affiliation:
Analysis Group
Saraswata Chaudhuri*
Affiliation:
McGill University and CIREQ
*
Address correspondence to Saraswata Chaudhuri, Department of Economics, McGill University and CIREQ, Montreal, QC, Canada; e-mail: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Attrition is monotonic when agents leaving multi-period studies do not return. Under a general missing at random (MAR) assumption, we study efficiency in estimation of parameters defined by moment restrictions on the distributions of the counterfactuals that were unrealized due to monotonic attrition. We discuss novel issues related to overidentification, usability of sample units, and the information content of various MAR assumptions for estimation of such parameters. We propose a standard doubly robust estimator for these parameters by equating to zero the sample analog of their respective efficient influence functions. Our proposed estimator performs well and vastly outperforms other estimators in our simulation experiment and empirical illustration.

Type
ARTICLES
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Footnotes

We are very grateful to the Editor (Peter C. B. Phillips), the Co-Editor (Patrik Guggenberger), two anonymous referees, and Whitney Newey for their help in improving the paper. We also thank Francesco Amodio, Marine Carrasco, Daniel Farewell, Bryan Graham, Fabian Lange, Steven Lehrer, Thierry Magnac, Erica Moodie, Chris Muris, Tom Parker, Geert Ridder, Youngki Shin, and various conference and seminar participants for helpful comments. Earlier versions of the paper were circulated under different names; e.g., “A note on efficiency in estimation with monotonically missing at random data.” The views presented in this work do not reflect those of Analysis Group. Analysis Group provided no financial support for this work.

References

REFERENCES

Abowd, J. M., Crepon, B., & Kramarz, F. (2001). Moment estimation with attrition: An application to economic models. Journal of the American Statistical Association , 96, 12231231.Google Scholar
Abrevaya, J., & Donald, S. G. (2017). A GMM approach for dealing with missing data on regressors and instruments. Review of Economics and Statistics , 99, 657662.Google Scholar
Achilles, C., Bain, H. P., Bellott, F., Boyd-Zaharias, J., Finn, J., Folger, J., Johnston, J., & Word, E. (2008). Tennessee’s Student Teacher Achievement Ratio (STAR) project.Google Scholar
Ackerberg, D., Chen, X., & Hahn, J. (2012). A practical asymptotic variance estimator for two-step semiparametric estimators. The Review of Economics and Statistics , 94, 481498.Google Scholar
Ackerberg, D., Chen, X., Hahn, J., & Liao, Z. (2014). Asymptotic efficiency of semiparametric two-step GMM. Review of Economic Studies , 81, 919943.Google Scholar
Bang, H., & Robins, J. M. (2005). Doubly robust estimation in missing data and causal inference models. Biometrics , 61, 962972.Google Scholar
Brown, B., & Newey, W. (1998). Efficient semiparametric estimation of expectations. Econometrica , 66, 453464.Google Scholar
Cao, W., Tsiatis, A., & Davidian, M. (2009). Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data. Biometrika , 96, 723734.Google Scholar
Chaudhuri, S. (2020). On efficiency gains from multiple incomplete subsamples. Econometric Theory , 36, 488525.Google Scholar
Chen, X., Hong, H., & Tarozzi, A. (2008). Semiparametric efficiency in GMM models with auxiliary data. Annals of Statistics , 36, 808843.Google Scholar
Chen, X., Linton, O., & van Keilegom, I. (2003). Estimation of semiparametric models when the criteria function is not smooth. Econometrica , 71, 15911608.Google Scholar
Chen, X., & Santos, A. (2018). Overidentification in regular models. Econometrica , 86, 17711817.Google Scholar
Chernozhukov, V., Escanciano, J.-C., Ichimura, H., Newey, W., & Robins, J. (2022). Locally robust semiparametric estimation. Econometrica , 90, 15011535.Google Scholar
Chetty, R., Friedman, J. N., Hilger, N., Saez, E., Schanzenbach, D. W., & Yagan, D. (2011). How does your kindergarten classroom affect your earnings? Evidence from Project STAR. The Quarterly Journal of Economics , 126, 15931660.Google Scholar
Dardanoni, V., Modica, S., & Peracchi, F. (2011). Regression with imputed covariates: A generalized missing-indicator approach. Journal of Econometrics , 162, 362368.Google Scholar
Ding, W., & Lehrer, S. F. (2010). Estimating treatment effects from contaminated multiperiod education experiments: The dynamic impacts of class size reductions. The Review of Economics and Statistics , 92, 3142.Google Scholar
Fitzgerald, J., Gottschalk, P., & Moffitt, R. (1996). An analysis of sample attrition in panel data: The Michigan Panel Study of Income Dynamics [NBER Working paper].Google Scholar
Gill, R. D., van der Laan, M. J., & Robins, J. M. (1997). Coarsening at random: Characterizations, conjectures and counterexamples. In Lin, D. Y., & Fleming, T. R. (Eds.), Proceedings of the first Seattle symposium in biostatistics: Survival analysis . Lecture Notes in Statistics (pp. 255294). Springer.Google Scholar
Graham, B. S. (2011). Efficiency bounds for missing data models with semiparametric restrictions. Econometrica , 79, 437452.Google Scholar
Hahn, J. (1998). On the role of the propensity score in efficient semiparametric estimation of average treatment effects. Econometrica , 66, 315331.Google Scholar
Hajek, J. (1971). Comment on a paper by D. Basu. In Godambe, V. R., & Sprott, D. A. (Eds.), Foundations of statistical inference (p. 236). Holt, Rinehert and Winston.Google Scholar
Hall, A. R., & Inoue, A. (2003). The large sample behaviour of the generalized method of moments estimator in misspecified models. Journal of Econometrics , 114, 361394.Google Scholar
Hanushek, E. A. (1999). Some findings from an independent investigation of the Tennessee STAR experiment and from other investigations of class size effects. Educational Evaluation and Policy Analysis , 21, 143163.Google Scholar
Hirano, K., Imbens, G., & Ridder, G. (2003). Efficient estimation of average treatment effects using the estimated propensity scores. Econometrica , 71, 11611189.Google Scholar
Holcroft, C., Rotnitzky, A., & Robins, J. M. (1997). Efficient estimation of regression parameters from multistage studies with validation of outcome and covariates. Journal of Statistical Planning and Inference , 65, 349374.Google Scholar
Hoonhout, P., & Ridder, G. (2019). Nonignorable attrition in multi-period panels with refreshment samples. Journal of Business and Economic Statistics , 37, 377390.Google Scholar
Horvitz, D., & Thompson, D. (1952). A generalization of sampling without replacement from a finite universe. Journal of American Statistical Association , 47, 663685.Google Scholar
Khan, S., & Tamer, E. (2010). Irregular identification, support conditions, and inverse weight estimation. Econometrica , 78, 20212042.Google Scholar
Krueger, A. B. (1999). Experimental estimates of education production functions. Quarterly Journal of Economics , 114, 497532.Google Scholar
Krueger, A. B., & Whitmore, D. M. (2001). The effect of attending a small class in the early grades on college-test taking and middle school test results: Evidence from Project STAR. The Economic Journal , 111, 128.Google Scholar
Muris, C. (2020). Efficient GMM estimation with incomplete data. Review of Economics and Statistics , 102, 518530.Google Scholar
Narain, R. D. (1951). On sampling without replacement with varying probabilities. Journal of Indian Soc. Agricultural Statistics , 3, 169174.Google Scholar
Newey, W. (1994). The asymptotic variance of semiparametric estimators. Econometrica , 62, 13491382.Google Scholar
Newey, W. K. (1990). Semiparametric efficiency bounds. Journal of Applied Econometrics , 5, 99135.Google Scholar
Nicoletti, C. (2006). Nonresponse in dynamic panel data models. Journal of Econometrics , 132, 461489.Google Scholar
Robins, J. M., & Gill, R. (1997). Non-response models for the analysis of non-monotone ignorable missing data. Statistics in Medicine , 16, 3956.Google Scholar
Robins, J. M., & Ritov, Y. (1997). Toward a curse of dimensionality appropriate (CODA) asymptotic theory for semi-parametric models. Statistics in Medicine , 16, 285319.Google Scholar
Robins, J. M., & Rotnitzky, A. (1992). Recovery of information and adjustment for dependent censoring using surrogate markers. In Jewell, N., Dietz, K., & Farewell, V. T. (Eds.), AIDS epidemiology: Methodological issues (pp. 297331). Birkhliuser.Google Scholar
Robins, J. M., & Rotnitzky, A. (1995). Semiparametric efficiency in multivariate regression models with missing data. Journal of American Statistical Association , 90, 122129.Google Scholar
Robins, J. M., Rotnitzky, A., & Zhao, L. (1994). Estimation of regression coefficients when some regressors are not always observed. Journal of American Statistical Association , 427, 846866.Google Scholar
Robins, J. M., Rotnitzky, A., & Zhao, L. (1995). Analysis of semiparametric regression models for repeated outcomes in the presence of missing data. Journal of American Statistical Association , 429, 106121.Google Scholar
Rothe, C., & Firpo, S. (2019). Properties of doubly robust estimators when nuisance functions are estimated nonparametrically. Econometric Theory , 35, 10481087.Google Scholar
Rotnitzky, A., & Robins, J. M. (1995). Semiparametric regression estimation in the presence of dependent censoring. Biometrika , 82, 805820.Google Scholar
Rubin, D. (1976). Inference and missing data. Biometrika , 63, 581592.Google Scholar
Scharfstein, D. O., Rotnitzky, A., & Robins, J. M. (1999). Adjusting for nonignorable drop-out using semiparametric nonresponse models. Journal of the American Statistical Association , 94, 10961146.Google Scholar
Tan, Z. (2007). Comment: Understanding OR, PS and DR. Statistical Science , 22, 560568.Google Scholar
Tsiatis, A. A. (2006). Semiparametric theory and missing data . Springer.Google Scholar
Vansteelandt, S., Rotnitzky, A., & Robins, J. M. (2007). Estimation of regression models for mean of repeated outcomes under nonignorable nonmonotone nonresponse. Biometrika , 94, 841860.Google Scholar
Wooldridge, J. M. (2002). Inverse probability weighted M-estimation for sample selection, attrition, and stratification. Portuguese Economic Journal , 1, 117139.Google Scholar
Wooldridge, J. M. (2010). Econometric analysis of cross section & panel data . MIT Press.Google Scholar
Supplementary material: File

Barnwell and Chaudhuri supplementary material

Barnwell and Chaudhuri supplementary material
Download Barnwell and Chaudhuri supplementary material(File)
File 429.2 KB